Finite Group Databasebeta

← C113×#16565 #43284585

Subgroups — C113×#16565 #43284585

Order 28928.

1258 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#395×C113C211yesmaximal, characteristic
2C2×#391×C113C211yesmaximal, characteristic
3C2×#387×C113C211yesmaximal, characteristic
4C2×#382×C113C211yesmaximal, characteristic
5C113×#1446C211yesmaximal, characteristic
6C113×#1445C212yesmaximal
7C113×#1443C212yesmaximal
8C113×#1442C211yesmaximal, characteristic
9C113×#1441C211yesmaximal, characteristic
10C113×#1441C212yesmaximal
11C113×#1441C212yesmaximal
12C23×Q8×C113C2211yescharacteristic
13C22×C4⋊C4×C113C2211yescharacteristic
14C22×C4⋊C4×C113C2212yes—
15C22×C4⋊C4×C113C2212yes—
16C22×C4⋊C4×C113C2211yescharacteristic
17C22×C4⋊C4×C113C2211yescharacteristic
18C22×C42×C113C2211yescharacteristic
19#395×C113—24no—
20#391×C113—24no—
21#387×C113—24no—
22#382×C113—24no—
23C2×#95×C113C2211yescharacteristic
24C2×#95×C113C2212yes—
25C2×#95×C113C2211yescharacteristic
26C2×#95×C113C2211yescharacteristic
27C2×#95×C113C2211yescharacteristic
28C2×#95×C113C2211yescharacteristic
29C2×#95×C113C2212yes—
30C2×#95×C113C2212yes—
31C2×#95×C113C2212yes—
32C2×#95×C113C2212yes—
33C2×#95×C113C2212yes—
34C2×#95×C113C2212yes—
35C2×#95×C113C2212yes—
36C2×#95×C113C2212yes—
37C2×#95×C113C2212yes—
38C2×#95×C113C2211yescharacteristic
39C22×Q8×C113—22no—
40C22×Q8×C113—22no—
41C22×Q8×C113—24no—
42C22×Q8×C113—22no—
43C22×Q8×C113—42no—
44C23×C4×C113C2311yescharacteristic
45C23×C4×C113C2312yes—
46C23×C4×C113C2312yes—
47C23×C4×C113C2311yescharacteristic
48C23×C4×C113C2311yescharacteristic
49C23×C4×C113C2312yes—
50C23×C4×C113C2311yescharacteristic
51C23×C4×C113C2311yescharacteristic
52C23×C4×C113C2312yes—
53C23×C4×C113C2311yescharacteristic
54C23×C4×C113C2311yescharacteristic
55C2×C4⋊C4×C113—22no—
56C2×C4⋊C4×C113—22no—
57C2×C4⋊C4×C113—24no—
58C2×C4⋊C4×C113—22no—
59C2×C4⋊C4×C113—22no—
60C2×C4⋊C4×C113—24no—
61C2×C4⋊C4×C113—22no—
62C2×C4⋊C4×C113—24no—
63C2×C4⋊C4×C113—24no—
64C2×C4⋊C4×C113—22no—
65C2×C4⋊C4×C113—42no—
66C2×C4⋊C4×C113—42no—
67C2×C4⋊C4×C113—42no—
68C2×C4⋊C4×C113Q814yescomplemented
69C2×C42×C113—22no—
70C2×C42×C113—22no—
71C2×C42×C113D414yes—
72#95×C113—24no—
73#95×C113—22no—
74#95×C113—22no—
75#95×C113—22no—
76#95×C113—22no—
77#95×C113—22no—
78#95×C113—24no—
79#95×C113—24no—
80#95×C113—24no—
81#95×C113—24no—
82#95×C113—42no—
83#95×C113—42no—
84#95×C113—42no—
85#95×C113—42no—
86#95×C113—42no—
87#95×C113D414yes—
88C24×C113C2411yescharacteristic
89C2×Q8×C113—28no—
90C2×Q8×C113—48no—
91C2×Q8×C113—48no—
92C2×Q8×C113—44no—
93C2×Q8×C113—44no—
94C22×C4×C113—21no—
95C22×C4×C113—21no—
96C22×C4×C113—22no—
97C22×C4×C113—21no—
98C22×C4×C113—22no—
99C22×C4×C113—21no—
100C22×C4×C113—21no—
101C22×C4×C113—21no—
102C22×C4×C113—21no—
103C22×C4×C113—22no—
104C22×C4×C113—21no—
105C22×C4×C113—22no—
106C22×C4×C113—21no—
107C22×C4×C113—21no—
108C22×C4×C113—21no—
109C22×C4×C113—22no—
110C22×C4×C113—22no—
111C22×C4×C113—21no—
112C22×C4×C113—22no—
113C22×C4×C113—22no—
114C22×C4×C113—22no—
115C22×C4×C113—21no—
116C22×C4×C113—22no—
117C22×C4×C113—22no—
118C22×C4×C113—22no—
119C22×C4×C113—22no—
120C22×C4×C113—22no—
121C22×C4×C113—22no—
122C22×C4×C113—22no—
123C22×C4×C113—22no—
124C22×C4×C113—22no—
125C22×C4×C113—21no—
126C22×C4×C113—21no—
127C22×C4×C113—21no—
128C22×C4×C113—22no—
129C22×C4×C113—22no—
130C22×C4×C113—21no—
131C22×C4×C113—22no—
132C22×C4×C113—22no—
133C22×C4×C113—21no—
134C22×C4×C113—22no—
135C22×C4×C113—22no—
136C22×C4×C113—21no—
137C22×C4×C113—22no—
138C22×C4×C113—22no—
139C22×C4×C113—22no—
140C22×C4×C113—22no—
141C22×C4×C113—22no—
142C22×C4×C113—22no—
143C22×C4×C113—22no—
144C22×C4×C113—22no—
145C22×C4×C113—22no—
146C22×C4×C113—22no—
147C22×C4×C113—22no—
148C22×C4×C113—21no—
149C22×C4×C113—22no—
150C22×C4×C113C2×D412yes—
151C22×C4×C113C2×D414yes—
152C22×C4×C113C2×D412yes—
153C22×C4×C113C2×D412yes—
154C22×C4×C113C2×D412yes—
155C22×C4×C113C2×Q812yes—
156C22×C4×C113C2×Q812yes—
157C22×C4×C113C2×Q812yes—
158C22×C4×C113#4114yes—
159C22×C4×C113#4112yes—
160C22×C4×C113#4112yes—
161C4⋊C4×C113—28no—
162C4⋊C4×C113—48no—
163C4⋊C4×C113—48no—
164C4⋊C4×C113—44no—
165C4⋊C4×C113—44no—
166C42×C113—28no—
167C23×C113C22×D411yescharacteristic
168C23×C113C22×D411yescharacteristic
169C23×C113C22×Q811yescharacteristic
170C23×C113C2×#4111yescharacteristic
171C23×C113C2×#4111yescharacteristic
172C23×C113C2×#4112yes—
173C23×C113H(5,𝔽2)12yes—
174C23×C113H(5,𝔽2)11yescharacteristic
175C23×C1132−1+412yes—
176C23×C1132−1+412yes—
177C23×C1132−1+411yescharacteristic
178Q8×C113—416no—
179C2×C4×C113—22no—
180C2×C4×C113—22no—
181C2×C4×C113—22no—
182C2×C4×C113—22no—
183C2×C4×C113—22no—
184C2×C4×C113—24no—
185C2×C4×C113—22no—
186C2×C4×C113—24no—
187C2×C4×C113—22no—
188C2×C4×C113—22no—
189C2×C4×C113—22no—
190C2×C4×C113—22no—
191C2×C4×C113—22no—
192C2×C4×C113—24no—
193C2×C4×C113—22no—
194C2×C4×C113—22no—
195C2×C4×C113—24no—
196C2×C4×C113—24no—
197C2×C4×C113—24no—
198C2×C4×C113—24no—
199C2×C4×C113—24no—
200C2×C4×C113—22no—
201C2×C4×C113—24no—
202C2×C4×C113—22no—
203C2×C4×C113—41no—
204C2×C4×C113—42no—
205C2×C4×C113—41no—
206C2×C4×C113—42no—
207C2×C4×C113—42no—
208C2×C4×C113—41no—
209C2×C4×C113—41no—
210C2×C4×C113—42no—
211C2×C4×C113—42no—
212C2×C4×C113—42no—
213C2×C4×C113—42no—
214C2×C4×C113—41no—
215C2×C4×C113—42no—
216C2×C4×C113—42no—
217C2×C4×C113—41no—
218C2×C4×C113—42no—
219C2×C4×C113—42no—
220C2×C4×C113—41no—
221C2×C4×C113—41no—
222C2×C4×C113—41no—
223C2×C4×C113—42no—
224C2×C4×C113—41no—
225C2×C4×C113—42no—
226C2×C4×C113—41no—
227C2×C4×C113—42no—
228C2×C4×C113—42no—
229C2×C4×C113—41no—
230C2×C4×C113—42no—
231C2×C4×C113—42no—
232C2×C4×C113—42no—
233C2×C4×C113—42no—
234C2×C4×C113—42no—
235C2×C4×C113—42no—
236C2×C4×C113—42no—
237C2×C4×C113—42no—
238C2×C4×C113—42no—
239C2×C4×C113—42no—
240C2×C4×C113—42no—
241C2×C4×C113—42no—
242C2×C4×C113—42no—
243C2×C4×C113—42no—
244C2×C4×C113#12114yes—
245C2×C4×C113C22⋊Q814yes—
246C22×C113C2×#12111yescharacteristic
247C22×C113C2×C22⋊Q811yescharacteristic
248C22×C113#52511yescharacteristic
249C22×C113#53511yescharacteristic
250C22×C113#53611yescharacteristic
251C22×C113#53611yescharacteristic
252C22×C113#53612yes—
253C22×C113#53711yescharacteristic
254C22×C113#54112yes—
255C22×C113#54112yes—
256C22×C113#54212yes—
257C22×C113#54212yes—
258C22×C113#54412yes—
259C22×C113#54612yes—
260C22×C113#54611yescharacteristic
261C22×C113D4×Q811yescharacteristic
262C22×C113#55112yes—
263C22×C113#55211yescharacteristic
264C22×C113#55411yescharacteristic
265C22×C113#55612yes—
266C22×C113#55712yes—
267C22×C113#56212yes—
268C22×C113#56312yes—
269C4×C113—24no—
270C4×C113—24no—
271C4×C113—42no—
272C4×C113—42no—
273C4×C113—44no—
274C4×C113—42no—
275C4×C113—44no—
276C4×C113—82no—
277C4×C113—81no—
278C4×C113—81no—
279C4×C113—82no—
280#16565C11311yesmaximal, characteristic, direct product factor, Sylow
281C2×C113#241111yescharacteristic
282C2×C113#241711yescharacteristic
283C2×C113#258111yescharacteristic
284C2×C113#262111yescharacteristic
285C2×C113#262811yescharacteristic
286C2×C113#263711yescharacteristic
287C2×C113#270012yes—
288C2×C113#271312yes—
289C2×C113#275512yes—
290C2×C113#276212yes—
291C2×C113#282011yescharacteristic
292C2×#395C2×C11311yescharacteristic
293C2×#391C2×C11311yescharacteristic
294C2×#387C2×C11311yescharacteristic
295C2×#382C2×C11311yescharacteristic
296#1446C2×C11311yescharacteristic
297#1445C2×C11312yes—
298#1443C2×C11312yes—
299#1442C2×C11311yescharacteristic
300#1441C2×C11311yescharacteristic
301#1441C2×C11312yes—
302#1441C2×C11312yes—
303C113#1656511yescharacteristic, direct product factor, Sylow
304C23×Q8C22×C11311yescharacteristic
305C22×C4⋊C4C22×C11311yescharacteristic
306C22×C4⋊C4C22×C11312yes—
307C22×C4⋊C4C22×C11312yes—
308C22×C4⋊C4C22×C11311yescharacteristic
309C22×C4⋊C4C22×C11311yescharacteristic
310C22×C42C22×C11311yescharacteristic
311#395—24no—
312#391—24no—
313#387—24no—
314#382—24no—
315C2×#95C22×C11312yes—
316C2×#95C22×C11311yescharacteristic
317C2×#95C22×C11312yes—
318C2×#95C22×C11312yes—
319C2×#95C22×C11311yescharacteristic
320C2×#95C22×C11311yescharacteristic
321C2×#95C22×C11311yescharacteristic
322C2×#95C22×C11312yes—
323C2×#95C22×C11312yes—
324C2×#95C22×C11311yescharacteristic
325C2×#95C22×C11312yes—
326C2×#95C22×C11312yes—
327C2×#95C22×C11312yes—
328C2×#95C22×C11312yes—
329C2×#95C22×C11312yes—
330C2×#95C22×C11311yescharacteristic
331C22×Q8—22no—
332C22×Q8—22no—
333C22×Q8—24no—
334C22×Q8—22no—
335C22×Q8—42no—
336C23×C4C23×C11311yescharacteristic
337C23×C4C23×C11312yes—
338C23×C4C23×C11312yes—
339C23×C4C23×C11311yescharacteristic
340C23×C4C23×C11312yes—
341C23×C4C23×C11311yescharacteristic
342C23×C4C23×C11311yescharacteristic
343C23×C4C23×C11311yescharacteristic
344C23×C4C23×C11312yes—
345C23×C4C23×C11311yescharacteristic
346C23×C4C23×C11311yescharacteristic
347C2×C4⋊C4—22no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—24no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—24no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—24no—
355C2×C4⋊C4—24no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—42no—
358C2×C4⋊C4—42no—
359C2×C4⋊C4—42no—
360C2×C4⋊C4Q8×C11314yescomplemented
361C2×C42—22no—
362C2×C42—22no—
363C2×C42D4×C11314yes—
364#95—24no—
365#95—22no—
366#95—22no—
367#95—22no—
368#95—22no—
369#95—22no—
370#95—24no—
371#95—24no—
372#95—24no—
373#95—24no—
374#95—42no—
375#95—42no—
376#95—42no—
377#95—42no—
378#95—42no—
379#95D4×C11314yes—
380C24C24×C11311yescharacteristic
381C2×Q8—28no—
382C2×Q8—48no—
383C2×Q8—48no—
384C2×Q8—44no—
385C2×Q8—44no—
386C22×C4—21no—
387C22×C4—21no—
388C22×C4—22no—
389C22×C4—21no—
390C22×C4—22no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—22no—
396C22×C4—21no—
397C22×C4—22no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—21no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—21no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—21no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—21no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—21no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—21no—
441C22×C4—22no—
442C22×C4C2×D4×C11312yes—
443C22×C4C2×D4×C11314yes—
444C22×C4C2×D4×C11312yes—
445C22×C4C2×D4×C11312yes—
446C22×C4C2×D4×C11312yes—
447C22×C4C2×Q8×C11312yes—
448C22×C4C2×Q8×C11312yes—
449C22×C4C2×Q8×C11312yes—
450C22×C4#41×C11314yes—
451C22×C4#41×C11312yes—
452C22×C4#41×C11312yes—
453C4⋊C4—28no—
454C4⋊C4—48no—
455C4⋊C4—48no—
456C4⋊C4—44no—
457C4⋊C4—44no—
458C42—28no—
459C23C22×D4×C11311yescharacteristic
460C23C22×D4×C11311yescharacteristic
461C23C22×Q8×C11311yescharacteristic
462C23C2×#41×C11311yescharacteristic
463C23C2×#41×C11311yescharacteristic
464C23C2×#41×C11312yes—
465C23H(5,𝔽2)×C11312yes—
466C23H(5,𝔽2)×C11311yescharacteristic
467C232−1+4×C11312yes—
468C232−1+4×C11312yes—
469C232−1+4×C11311yescharacteristic
470Q8—416no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—24no—
477C2×C4—22no—
478C2×C4—24no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—24no—
485C2×C4—22no—
486C2×C4—22no—
487C2×C4—24no—
488C2×C4—24no—
489C2×C4—24no—
490C2×C4—24no—
491C2×C4—24no—
492C2×C4—22no—
493C2×C4—24no—
494C2×C4—22no—
495C2×C4—41no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—41no—
499C2×C4—42no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—41no—
508C2×C4—42no—
509C2×C4—41no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—42no—
516C2×C4—41no—
517C2×C4—42no—
518C2×C4—41no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—41no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4#121×C11314yes—
537C2×C4C22⋊Q8×C11314yes—
538C22C2×#121×C11311yescharacteristic
539C22C2×C22⋊Q8×C11311yescharacteristic
540C22#525×C11311yescharacteristic
541C22#535×C11311yescharacteristic
542C22#536×C11311yescharacteristic
543C22#536×C11311yescharacteristic
544C22#536×C11312yes—
545C22#537×C11311yescharacteristic
546C22#541×C11312yes—
547C22#541×C11312yes—
548C22#542×C11312yes—
549C22#542×C11312yes—
550C22#544×C11312yes—
551C22#546×C11312yes—
552C22#546×C11311yescharacteristic
553C22D4×Q8×C11311yescharacteristic
554C22#551×C11312yes—
555C22#552×C11311yescharacteristic
556C22#554×C11311yescharacteristic
557C22#556×C11312yes—
558C22#557×C11312yes—
559C22#562×C11312yes—
560C22#563×C11312yes—
561C4—24no—
562C4—24no—
563C4—42no—
564C4—42no—
565C4—44no—
566C4—42no—
567C4—44no—
568C4—82no—
569C4—81no—
570C4—81no—
571C4—82no—
572C2C113×#241111yescharacteristic
573C2C113×#241711yescharacteristic
574C2C113×#258111yescharacteristic
575C2C113×#262111yescharacteristic
576C2C113×#262811yescharacteristic
577C2C113×#263711yescharacteristic
578C2C113×#270012yes—
579C2C113×#271312yes—
580C2C113×#275512yes—
581C2C113×#276212yes—
582C2C113×#282011yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C113C24
commutator, Frattini, cosocleC24C24×C113
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C113 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
68. C2×C4⋊C4×C113Q8semidirect
280. #16565C113direct (N × H)
303. C113#16565direct (N × H)
360. C2×C4⋊C4Q8×C113semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#395×C1132
C2×#391×C1132
C2×#387×C1132
C2×#382×C1132
C113×#14462
C113×#14452
C113×#14432
C113×#14422
C113×#14412
#16565113